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Let $M_n(\mathbb{C})$ represent the space of $n \times n$ matrices over $\mathbb{C}$. We will think of it as a $\mathbb{C}$-vector space. Notice that if $A \in M_n(\mathbb{C})$ is invertible, then the ...

Is there a simple way to parametrize the orthogonal group O(3) of 3 by 3 orthogonal matrices?